Checking the reliability of a linear-programming based approach towards detecting community structures in networks

Chen, W.Y.C.; Dress, Andreas; Yu, Winking Q.

doi:10.1049/iet-syb:20060076

Cited by 6 publications

(5 citation statements)

References 40 publications

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“…also [79]), eco-efficiency in logistics networks [74], the understanding of community structures [19], aspects of lifestyle and awareness, the sustainable development of our societies [36], and educational measurements as well. Socio-econo-environment networks can become an expression of such an extension, which might be called "soft" today but can be in the range and service of applied mathematics tomorrow.…”

Section: Resultsmentioning

confidence: 99%

A New Mathematical Approach in Environmental and Life Sciences: Gene–Environment Networks and Their Dynamics

Weber¹,

Gök

Söyler

2008

Environ Model Assess

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An important research area in life sciences is devoted to modeling, prediction, and dynamics of geneexpression patterns. As clearly understood in these days, this enterprise cannot become satisfactory without acknowledging the role of the environment. To a representation of past, present, and most likely future states, we also encounter measurement errors and uncertainties. This paper surveys and improves recent advances in understanding the foundations and interdisciplinary implications of the newly introduced geneenvironment networks, and it integrates the important theme of carbon dioxide emission reduction into the networks and dynamics. We also introduce some operational and managerial issues of practical working and decision making, expressed in terms of sliding windows, quadrants (modules) of parametric effects, and navigating (controlling) between such effects and directing them. Given data from DNA microarray experiments and environmental records, we extract nonlinear ordinary differential equations that contain parameters that have to be determined. For this, we employ modern (Chebychevian) approximation and (generalized semi-infinite) optimization. After this is provided, timediscretized dynamical systems are studied. A combinatorial algorithm with polyhedra sequences allows to detect the region of parametric stability. Finally, we analyze the topological landscape of gene-environment networks with its structural (in)stability. By embedding as a module and investigating CO 2 emission control and figuring out game theoretical aspects, we conclude. This pioneering work is theoretically elaborated, practically devoted to health care, medicine, education, living conditions, and environmental protection, and it invites the readers to future research.

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Section: Resultsmentioning

confidence: 99%

A New Mathematical Approach in Environmental and Life Sciences: Gene–Environment Networks and Their Dynamics

Weber¹,

Gök

Söyler

2008

Environ Model Assess

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“…Our algorithm reveals their relationships quite well, but we skip the results here (to be published -together with results obtained for simulated data -elsewhere [12] and available upon request) and, instead, shortly discuss the time complexity of our approach:…”

Section: Resultsmentioning

confidence: 99%

“…However, if we put N := 3 (as the latter two methods really suggest that there should be three communities), the METIS-algorithms produce, not unexpectedly, more mistakes. Measuring the number of mistakes using the "single-element transfer distance" introduced by Charon et al [11] (also discussed in [12]), for kmetis the distance is 12, and for pmetis the distance is 9.…”

Section: Resultsmentioning

confidence: 99%

Community Structures of Networks

Chen

Dress

2008

Math.comput.sci.

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Abstract. We present an approach to studying the community structures of networks by using linear programming (LP). Starting with a network in terms of (a) a collection of nodes and (b) a collection of edges connecting some of these nodes, we use a new LP-based method for simultaneously (i) finding, at minimal cost, a second edge set by deleting existing and inserting additional edges so that the network becomes a disjoint union of cliques and (ii) appropriately calibrating the costs for doing so. We provide examples that suggest that, in practice, this approach provides a surprisingly good strategy for detecting community structures in given networks. Mathematics Subject Classification (2000). 90C35, 90C90, 68W25.

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“…Researchers from various disciplines analyze community structure using eigenvectors and sparse matrix formulations [23], algebraic connectivity [24], partitioning techniques [25], small-world effect [12], parameterized linear programming [26], and many other methods. These approaches provide better results, but are computationally expensive as they require global information of the network.…”

Section: Overviewmentioning

confidence: 99%

Community Detection in Biological Networks

Thakur

2011

Applied Statistics for Network Biology

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Networks are everywhere and evolving in various forms, following certain characteristic patterns like small-world and scale-free characteristics. The basis of these forms is not the random addition of nodes and vertices to the system under study, but a systematic process of mutual evolution. This makes many aspects of such systems worth studying. Researchers have invested many years interpreting such systems, for instance how biological networks evolve and why humans form societies to name a few. Thus, seminal to the behavior to these systems are the way internal components are connected to each other. These connections breed structures that exemplify the nature and the behavior of the overall system. Advances in genomics have generated enormous amounts of data, currently gathered by biologists and now available to the scientific community at large. The categorization of this data naturally falls into various classes, ranging from protein sequences to complex molecules. Thus, challenges lie in understanding the properties and dynamics of such complex systems rather than gaining insight into the individual components. Fortunately, promises shown in statistical physics and network theory that offer a host of methods and tools to analyze large data can invariably be used in biology. Modeling interactions between proteins, cells, and other genomic data as network graphs and applying statistical techniques on them can greatly benefit us in scrutinizing the intricacies that exist in these datasets. These methods not only simplify the representations, but also aid in searching for general principles of organization and evolution of biological structures. For example, smallworld analysis is used to explain protein-protein interaction networks and scale-free invariance properties exist for in silico evolution of metabolic networks, which encode an increasing amount of information about their environment. The questions often arises as to which properties of such systems are worth studying and how are the emergent behaviors actually affecting the overall functionality of such systems. Visualization is a potential tool that was used as a first step to display the connectivity patterns between various components and describe the structure as a whole. Another

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Checking the reliability of a linear-programming based approach towards detecting community structures in networks

Cited by 6 publications

References 40 publications

A New Mathematical Approach in Environmental and Life Sciences: Gene–Environment Networks and Their Dynamics

A New Mathematical Approach in Environmental and Life Sciences: Gene–Environment Networks and Their Dynamics

Community Structures of Networks

Community Detection in Biological Networks

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